How do you factor a perfect square trinomial?

A perfect square trinomial of the form $$x^2 + 2bx + b^2$$ factors to $$(x + b)^2$$ .

What is the quadratic formula?

The quadratic formula is $$x = \frac{-b \textpm \textsqrt{b^2 - 4ac}}{2a}$$ , used to find the roots of a quadratic equation.

What is the discriminant in a quadratic equation?

The discriminant is the part of the quadratic formula under the square root, given by $$b^2 - 4ac$$ . It determines the nature of the roots.

What does a positive discriminant indicate?

A positive discriminant indicates that the quadratic equation has two distinct real roots.

What does a zero discriminant indicate?

A zero discriminant indicates that the quadratic equation has exactly one real root (a repeated root).

What does a negative discriminant indicate?

A negative discriminant indicates that the quadratic equation has no real roots, but two complex roots.

What is a common mistake when completing the square?

A common mistake is incorrectly adding or subtracting the squared term, leading to an incorrect equation.

How can you verify your solution after completing the square?

You can verify your solution by substituting the found values back into the original equation to check if they satisfy it.

What is the relationship between the vertex and the axis of symmetry in a quadratic function?

The vertex of a quadratic function lies on the axis of symmetry, which is the vertical line given by $$x = h$$ , where (h, k) is the vertex.

Completing the Square Flashcards

Student preview

16 questions

Show all answers

1.

FLASHCARD QUESTION

Front

What is 'completing the square'?

Back

Completing the square is a method used to solve quadratic equations by rewriting them in the form of a perfect square trinomial, which makes it easier to solve for the variable.

Tags

CCSS.HSA-REI.B.4B

2.

FLASHCARD QUESTION

Front

What is the standard form of a quadratic equation?

Back

3.

FLASHCARD QUESTION

Front

How do you find 'c' when completing the square?

Back

Tags

CCSS.HSA-REI.B.4B

4.

FLASHCARD QUESTION

Front

What is the vertex form of a quadratic equation?

Back

5.

FLASHCARD QUESTION

Front

What is the first step in completing the square?

Back

The first step is to move the constant term to the other side of the equation.

Tags

CCSS.HSA-REI.B.4B

6.

FLASHCARD QUESTION

Front

What do you do after moving the constant term when completing the square?

Back

Tags

CCSS.HSA-REI.B.4B

7.

FLASHCARD QUESTION

Front

What is the purpose of adding the squared term when completing the square?

Back

Adding the squared term allows you to form a perfect square trinomial, which can be factored easily.

Tags

CCSS.HSA-REI.B.4B

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